Short-to-Long: Detached Features for Long-Horizon Value Learning
Organizations: NVIDIA Research
Abstract
Learning useful representations from continually changing value targets remains a challenge in deep reinforcement learning. We study the temporal horizon of this supervision: smaller discounts make these targets less sensitive to distant bootstrap changes, but using them for behavior changes the control objective. We introduce Short-to-Long (S2L), which supplies a long-horizon behavior learner with features trained by smaller-discount source networks. Detached connections prevent the behavior value loss from updating the sources, allowing each source to follow its own value objective while the behavior discount remains unchanged. Across Atari, online continuous control, and offline continuous control, the approach yields aggregate performance gains, improving the paired terminal median on 40 of 57 Atari games. Matched Atari ablations support the roles of feature transfer, smaller source discounts, and gradient isolation. Fixed-trajectory measurements further show reduced drift in source value targets with mixed discounts.
Figures & tables
| Subset | Final return | AUC | ||||
|---|---|---|---|---|---|---|
| Mean | W | 0–1M | 500k–1M | 750k–1M | ||
| All | 720 | 39.09 | 465 | 7.16 | 27.03 | 34.99 |
| DDPG | 360 | 47.42 | 242 | 17.29 | 40.66 | 46.66 |
| SAC | 360 | 30.76 | 223 | 13.40 | 23.31 | |
| AdamW | 360 | 47.49 | 252 | 16.84 | 36.61 | 42.79 |
| Kron | 360 | 30.68 | 213 | 17.45 | 27.18 | |
| Metric | S2L-4 | SimBa | Paired W/L/T |
|---|---|---|---|
| Local fluctuation (detrended MAD) | 12.08 | 16.17 | 404/316/0 |
| Normalized maximum drawdown | 0.137 | 0.164 | 426/276/18 |
| Cumulative negative change | 38.26 | 45.32 | 412/290/18 |
| Worst 50k-step drop | 23.85 | 26.62 | 415/287/18 |
| Target drift | Mean | Median | Pairs | Games |
|---|---|---|---|---|
| Normalized (primary) | ||||
| Raw RMS (secondary) |
| (a) Original reference scores | |||
|---|---|---|---|
| Method | Endpoint HNS | Full AUC | Second-half AUC |
| Scaled PQN | |||
| S2L-4 | |||
| (b) Variant minus full S2L-4 | |||
| Variant | endpoint | full AUC | second-half AUC |
| No gradient isolation | |||
| Summary | Pair wins | Game wins | IQM | 95% CI |
|---|---|---|---|---|
| Terminal HNS | 147/228 | 35/57 | +.0323 | |
| Full-training AUC | 149/228 | 39/57 | +.0188 | |
| Late-half AUC | 153/228 | 39/57 | +.0250 | |
| Terminal last-10 | 152/228 | 38/57 | +.0329 |
| Environment | Simple | Medium | Expert | Mean |
|---|---|---|---|---|
| HalfCheetah | (0/5) | (5/5) | (5/5) | (10/15) |
| Hopper | (5/5) | (3/5) | (2/5) | (10/15) |
| Walker2d | (1/5) | (4/5) | (3/5) | (8/15) |
| All | (6/15) | (12/15) | (10/15) | (28/45) |
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
| Setting | Value |
|---|---|
| Algorithm | PQN with Q( ) |
| Main / short discount | .99 / .90 |
| .65 | |
| CNN | Atari, medium: 32–64–64 channels |
| MLP | width 2560, five two-linear residual blocks |
| Stabilizers | full MultiSkip, LayerNorm, Kron |
| Qbert (4 seeds) | Phoenix (4 seeds) | Pooled (8) | ||||
|---|---|---|---|---|---|---|
| Transferred feature | GM | Wins | GM | Wins | GM | Wins |
| None (baseline) | 1.000 | – | 1.000 | – | 1.000 | – |
| Short input | 1.173 | 4/4 | 1.173 | 4/4 | 1.173 | 8/8 |
| Aligned absolute | 1.239 | 4/4 | 1.237 | 4/4 | 1.238 | 8/8 |
| Aligned delta | 1.188 | 4/4 | 1.199 | 4/4 | 1.194 | 8/8 |
| Dense all-layer mean | 1.277 | 4/4 | 1.240 | 4/4 | 1.258 | 8/8 |
| Transferred feature | Qbert GM | Phoenix GM | Pooled GM | Positive pairs |
|---|---|---|---|---|
| Short input | 1.000 | 1.000 | 1.000 | – |
| Aligned absolute | 1.0565 | 1.0546 | 1.0556 | 6/8 |
| Aligned delta | 1.0129 | 1.0221 | 1.0175 | 4/8 |
| Dense all-layer mean | 1.0887 | 1.0566 | 1.0725 | 6/8 |
| Prefix mean | 1.0420 | 1.0773 | 1.0595 | 7/8 |
| Game | Selected | Effective horizon | Median SNI |
|---|---|---|---|
| Qbert | .875 | 8 | .256 |
| Phoenix | .900 | 10 | .154 |
| Asterix | .875 | 8 | .106 |
| Breakout | .984375 | 64 | .064 |
| Seaquest | .96875 | 32 | .341 |
| Contrast | Endpoint HNS | Full AUC | Second-half AUC |
|---|---|---|---|
| Transfer no transfer | |||
| Mixed discounts all | |||
| Detached backpropagated |
| Summary | S2L-4 | MDH-4 | MDH-4 (wide) |
|---|---|---|---|
| Parameters (approx.) | 321.4M | 80.4M | 321.4M |
| Endpoint HNS | |||
| Full-training AUC | |||
| Late-half AUC | |||
| Terminal last-10 |
| Setting | Value |
|---|---|
| Tasks | dog-run, dog-trot, humanoid-run, humanoid-walk |
| Algorithms / optimizers | SAC, DDPG / AdamW, Kron |
| Environment steps / action repeat | 1,000,000 / 2 |
| Train environments / updates per interaction | 1 / 2 |
| Replay capacity / warm-up / batch | 1M / 5,000 / 256 |
| Evaluation | 10 episodes every 50,000 environment steps |
| Game | Seed | A | B | E | F |
|---|---|---|---|---|---|
| Qbert | 1 | 4.194 | 4.888 | 5.754 | 5.532 |
| 2 | 3.973 | 5.363 | 5.330 | 4.760 | |
| 3 | 4.722 | 4.950 | 5.468 | 5.138 | |
| 4 | 4.365 | 5.003 | 5.441 | 5.658 | |
| Phoenix | 1 | 6.956 | 8.190 | 8.086 | 8.430 |
| 2 | 6.972 | 8.464 | 8.619 | 8.576 |
Reinforcement Learning
Reinforcement learning studies how agents learn sequential decisions from rewards and interaction, balancing exploration, performance, safety, and adaptation.
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